Single Degree-of-Freedom Exoskeleton Mechanism Design for ThumbRehabilitation*

Yimesker Yihun, Robert Miklos, Alba Perez-Gracia,1David J. Reinkensmeyer2, Keith Denney and Eric T. Wolbrecht3

Abstract This paper presents the kinematic design of aspatial, 1-degree-of-freedom closed linkage to be used as anexoskeleton for thumb motion. Together with an already-designed finger mechanism, it forms a robotic device for handtherapy. The goal for the exoskeleton is to generate the desiredgrasping and pinching path of the thumb with one degree offreedom, rather than using a system actuating all its jointsindependently. In addition to the path of the thumb, additionalconstraints are added in order to control the position and sizeof the exoskeleton, reducing physical and sensory interferencewith the user.

I. INTRODUCTIONRobotic devices have been shown to be capable of au-

tomating the strenuous and repetitive nature of movementtherapy after stroke or other neurological injury (for anintroduction, see [1], [2]). Additionally, robotic devices givescientists a new investigative tool for recording progressduring movement training and for determining the factorsthat promote functional recovery. Of particular interest isthe ability to design, implement, and test assistive controlstrategies. Many different control strategies have been de-veloped (see review: [3]). The most promising approachesfall into the assist-as-needed category, where an attempt ismade to vary the level of assistance to match the impairmentlevel of the patient. For example, [4] presents an assist-as-needed controller that learns a model of the patients abilitieswhile simultaneously reducing assistance when the patientperforms well. The result is a robotic device that can helppatients complete movements but continuously challengesthem to try. The efficacy of these and other control strategieshas been documented ([5], [6], [7]) but it remains unclearwhat specific controller characteristics increase patient learn-ing during therapy.

Proper evaluation of assist-as-needed control strategies isdependent upon the abilities of the robotic device. Ideally,the device would be able to apply any force at any speedat any location along the movement trajectory. In practice,

*This work was partially supported by Grant Number NIH-R01HD062744-01 from NCHHD, and by the US Department of the Army,award number W81XWH-10-1-0128 awarded and administered by the U.S.Army Medical Research Acquisition Activity. The content is solely theresponsibility of the authors.

1Dept. of Mechanical Engineering, Idaho State University, Pocatello,ID, USA. yihuyime@isu.edu, miklrobe@isu.edu,perealba@isu.edu

2Departments of Mechanical and Aerospace Engineering, Anatomy andNeurobiology, and Biomedical Engineering, University of California, Irvine,Irvine, CA, USA. dreinken@uci.edu

3Department of Mechanical Engineering, University of Idaho, Moscow,ID, USA. kmdenney@gmail.com, ewolbrec@uidaho.edu

this is impossible, but can be approached in a roboticdevice by keeping apparent inertia and friction low, and thecontrollable force bandwidth high. To achieve these features,we are developing an exoskeleton device for the fingers andthumb, with the actuators mounted along the forearm wheretheir effect on device inertia is minimized. In addition, theactuators are high-speed, low-friction linear motors, whichallows for high-bandwidth control. These characteristics havenot been fully achieved in previous robotic hand and wristdevices, including end-effector, glove, and exoskeleton typedevices ([8], [9], [10]).

The device presented in this paper is obtained following anew methodology for the design of exoskeletons. Tradition-ally, exoskeletons are designed so that they try to align withthe human joint axes of motion [8]. This assumes that thelocation of the axis can be accurately known, and in addition,that such a fixed axis exists for the range of motion of thejoint or set of joints, which is not always the case. A clearexample of complex kinematic modeling is the thumb, forwhich precise detection methods such as MRI segmentation[11] show that considering fixed rotational axes, especiallyfor the CMC joint, is not a good approximation; see also [12].Using the methodology described in this paper, based onkinematic synthesis, it is not necessary to know the geometryof the hand, but rather to have a description of its motion atthe point of attachment.

To meet the design needs for the rehabilitation applica-tion described above, a lightweight single-degree-of freedommechanism has been selected for following the paths of thethumb during simple pinch and grasping movements. Thecomplete exoskeleton device consists of two separate singledegree-of-freedom exoskeleton mechanisms: one for fingercurling motions, whose design was presented in [13], andone for thumb motions, presented in this paper. The resultingrobot will be able to assist in common, naturalistic fingerand thumb motions. As such, the therapy delivered shouldtranslate to a wide range of functional tasks, even if thedegrees-of-freedom of the robot are minimal.

The linkage to perform the thumb motion was selectedamong several single-degree-of-freedom spatial closed link-ages with four to six links, with a single end-effector forcontrolling the orientation and position of the proximalphalanx of the thumb. In this approach, the mechanismwill be actuated with a single actuator, and so the designof the mechanism is responsible for appropriately shapingthe thumb motion. In addition, the designed mechanism isconfined to the back of the hand, so as to minimize sensory

feedback interference, and to allow the mechanism to bemanufactured with minimal size. This combined with theintended location of the actuators will allow the device to beconstructed with low apparent inertia.

II. THUMB MECHANISM DESIGNA. Design objectives

The human thumb presents a complex 3D motion thatcan be modeled, depending on the needed accuracy, withthree to four degrees of freedom, and using variable jointaxes. For this project, the targeted task of the thumb is asingle spatial path going from index pinching to contactingthe tip of the fingers. We postulate that it is still possibleto use simplified, low-dof linkages for assisting in thismotion. We focus on a set of closed, spatial overconstrainedand non-overconstrained four-bar to six-bar linkages withlow mobility that present the desired characteristics for thisapplication, see [14] and [15]. The spatial mechanism is tobe attached to the proximal phalanx of the thumb. The goalis to find a single-dof mechanism whose path is as close tothe experimental thumb path as possible, while complyingwith additional size and placement constraints.

B. Thumb dataThe method is based on synthesize a linkage to follow as

closely as possible experimental paths of the human thumb.The thumb data was acquired using a Vicon motion trackingsystem. The set up we used had eight infrared cameras setaround the room, primarily for larger applications; howeverit worked very well for the hand motions. The markers thatare used with the system are small white balls that reflectthe inferred light. We used arrays with the markers placed1.25 inches apart making it easy to collect data in the threedimensions. In order to assess the exact location of the fixedlink with respect to the hand, additional sets of sensors areplaced on the arm, see Figure 1

Fig. 1. Markers placed in the thumb and data capture setup

The several experimental paths so obtained were separatedfor clarity; Figure 2 shows one typical point path, seen fromthe reference frame of the motion capture system.

For the design of spatial motion, it is sometimes advan-tageous to work with relative displacements. Each relativedisplacement expresses a motion of the thumb from a refer-ence configuration, taken as the thumb position at the firstframe. Each displacement can be modeled as an axis, plusa rotation about and a translation along the axis. We encodethis information as a screw, where the screw axis is the axisof the displacement and the pitch is the ratio of translationto rotation for that displacement.

Fig. 2. Thumbs proximal phalanx point path

Fig. 3. Thumbs proximal phalanx path: screw surface of relative screwaxes

Figure 3 shows the displacements of the thumbs proximalphalanx path as screw axes with a pitch, where the screwlengths are proportional to the pitch. The screw axes ofthe displacements with their pitches generate a screw hyper-surface. This representation has all the information of themotion except for the value of the rotation, which can becalculated independently.

C. Mechanism SelectionIn order to accomplish simplicity together with spatial

motion under a one-degree-of-freedom system, an initial setof closed spatial linkages with four to six links and standardrevolute (R), prismatic (P) and cylindrical (C) joints hasbeen selected. Some of these linkages are overconstrained,while others are trivial linkages, all of them with mobilityequal to one [14], [15]. Figure 4 shows the topology of thespatial CCCC linkage (a linkage with four cylindrical joints);candidate linkages with four links are particular cases of thisone, obtained by making some of the joint variables (i, ri)constant.

Similarly, the closed, spatial CCC-CCC linkage can beseen as the general case for the six-bar candidate linkages,see Figure 5. In particular, the following four-bar linkages:

Fig. 4. A spatial 4-bar CCCC linkage

Fig. 5. A spatial 6-bar CCCCCC linkage

RC-CC, RP-RP, RR-RR, and the following six-bar linkage:CRR-RRR were selected as candidates. Here, the dash sepa-rating joints indicates where the end-effector, or attachmentto the thumb, is being placed.

In order to asses the suitable topology for the thumblinkage, the workspace of relative displacements has beenanalyzed for each of these linkages. Figure 6 shows a typicalworkspace for the candidate linkage.

From inspection of the workspace shape, the candidatelinkages to be used for dimensional synthesis are the RR-RR, the RC-CC and the CRR-RRR. The RRRR is anoverconstrained linkage, while the other two present trivialmobility equal to one.

Among the properties of these linkages that are usefulfor our application we can cite the 1-dof motion, requiringonly one actuator, and topological simplicity while creating acomplex motion. In addition, overconstrained linkages haveother advantages, such as inherent structural rigidity.

D. Mechanism Design EquationsIn this section, the design equations corresponding to the

CRR-RRR mechanism are presented. The reason to do so isthat it turned out to give the most fitted mechanisms for thetask.

Let us consider the closed CRR-RRR linkage as two serialchains, CRR and RRR, joined at their end-effectors. The axesare labeled as shown in Figure 5, starting at the fixed C jointand going around up to the final fixed R joint. For everyjoint i, let Si = si + s0i be the joint axis, with rotation i,and slide (for the C joint only) di. We express the forward

Fig. 6. Workspaces of the CCCR, the RRRR, the RPRP linkages

kinematics equations of the CRR and RRR chains using dualquaternions [16],

QCRR(1,2,3) =

3

i=1

(cosi2

+ sini2

Si)

QRRR(6,5,4) =

i{6,5,4}

(cosi2

+ sini2

Si)

(1)wherei = i + di is the dual angle, and all di = 0except d1 corresponding to the cylindrical joint. The forwardkinematics so expressed represent the set of relative displace-ments of the chain with respect to a reference configuration.

In order to create the design equations, we minimizethe distance between the displacements captured in SectionII.B. and the displacements of the candidate chain. Weperform dimensional synthesis, that is, the goal is to findthe location and dimensions of the mechanism that performsapproximately the task.

The design equations are created by equating the forwardkinematics of the mechanism to each of the discrete positionsobtained from the motion capture. If we denote each finitedisplacement of the thumb as P i, we can create the relativedisplacements with respect to the first position of the thumb,P 1i = P i(P 1)1, to yield design equations

QCRR(i1,i

2,i

3) = P 1i,

QRRR(i6,

i5,

i4) = P

1i, i = 2, . . . ,m. (2)In these equations, the variables we are interested in

are what we call the structural variables, which are thePlucker coordinates of the joint axes Si = si + s0i at thereference configuration. In addition, the optimization processoutputs the angles of the chains in order to reach the thumbdisplacements.

To complete the system of equations in (2), we impose sizeconstraints on the mechanism so that it can be attached to the

lower arm and with reasonable dimensions. In particular, forthe six-link CRR-RRR mechanism, we add the constraints ofdistance between both fixed axes and also between the fixedaxes and the thumb,

S1 S6 = cos+ a sin

S1 P1 = cos + b sin (3)

where P1 is the screw axis of the first thumb position, and wefix the distance between the axes along the common normal,a, to a value between 50mm and 150mm, and the distancebetween the thumb attachment and the coupler axes, b, tosimilar values.

E. Implementation of the Design EquationsTen positions were selected from the thumb path, and the

first frame was taken as the reference configuration. Eachforward kinematics equality is composed of 8 equations, andforward kinematics are written for both serial chains com-posing the mechanism. This gives a total of 144 nonlinearequations. In addition, we have the constraints of (3). Overall,we have 147 equations.

The variables to solve for are the Plucker coordinatesof the axes, that is, six parameters per axis, and the jointvariables to reach each thumb position. The total is 97unknowns.

The equations were solved using a Levenberg-Marquardtnonlinear, unconstrained solver implemented in Java. This isbased on public domain MINPACK routines, translated fromFORTRAN to Java by Steve Verrill [17].

III. RESULTSThe best results were obtained for the CRR-RRR mecha-

nism. One of the sets of ten equally-spaced positions selectedfrom the thumb data can be seen in Figure 9. The equationswere run 14 times for three different sets of positions chosenfrom the thumb frames. The distance to the desired path hasbeen optimized by minimizing the distance at each step. Theoverall error of the function was smaller than 0.03, and ittook a variable amount of time, from a few minutes to a fewhours, to find solutions. For these 14 runs, 14 considerablydifferent solutions were found.

Out of these 14 solutions, 2 linkages were selected becauseof their overall dimensions and placement on the hand.Figure 7 shows the SolidWorks model of those solutions,named candidate I and II.

As overall solution, we selected the mechanism withthe best combination of fit to the path, dimensions andplacement. Due to the potentially very large number ofsolutions for this problem, not all the solution space hasbeen searched and hence we cannot assume that the selectedcandidate is the optimal one, but rather an acceptable one.

Figures 8 and 9 present the actual motion of the linkage ascompared to the thumb path and design poses. Even thoughthere is some small divergence in the paths, we must pointout that it is of the order of the variability of the several pathsobserved in the motion capture data, rendering an overallmotion that is within the normal thumb actuation.

Fig. 7. The two solutions selected for prototyping

Rapid prototypes have been built in order to assess themanufacturing and to better design the hand attachment andcompatibility with the finger exoskeleton. Figure 10 showsone of the prototype linkages mounted on the hand.

IV. CONCLUSIONS AND FUTURE WORKThis paper presents a task-oriented design methodology

for exoskeletons. Previous work targeted planar motion,while this paper focuses on the application to spatial motion.In particular, we apply the methodology to develop a 1-dofthumb exoskeleton for rehabilitation. The kinematic designis followed by a detailed mechanical design and prototyping.

The main advantage of this method with respect to pre-vious exoskeleton designs is that it does not need anyassumption about location and type of joints in the subject;the exoskeleton is going to follow the path that is selected astask regardless of the skeleton structure that generates it. Thisallows for the creation of new and innovative exoskeletondesigns. The high number of solutions obtained mean morechoices for the designer regarding placement, size, andinertia of the exoskeleton.

The final designs presented in this paper have been testedfor the desired path and the results seem to be acceptable.The placement of the mechanism on the lower arm and closeto the wrist is also according to specifications.

The next step is the force analysis of the mechanism. Thisis important because of the spatiality of the linkage, and willallow us to determine the best joint to place the actuator.

Fig. 8. One of the thumb paths (thin frames) with superimposed linkagepath (thick lines)

Fig. 9. Comparison between design positions (thin lines) and linkagepositions (thick lines)

Future research for the mechanism optimization includesidentifying a small subset of structural variables that, whenmodified, will produce a new mechanism to track a similarpath created by a slightly different thumb. In a fashion similarto [18], this will allow the mechanism to be re-configured tovarying subject sizes.

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